Q2) EXAMPLE WIT RMAL RANDUM VARIABLE: turn in the printout Suppose the random variable "height" has a normal distribution with mean 67 and variance of 14. Use the rnorm() function to draw three random samples from this population with the sizes 10, 1000 and 1000,000 respectively. Calculate the sample mean in each case and show that as n increases the sample mean approaches the true population mean. Reminder: The "RNORMAL" function in R: RNORMAL (# sample size, mean = # population mean: sd = # population standard deviation)
Q2) EXAMPLE WIT RMAL RANDUM VARIABLE: turn in the printout Suppose the random variable "height" has a normal distribution with mean 67 and variance of 14. Use the rnorm() function to draw three random samples from this population with the sizes 10, 1000 and 1000,000 respectively. Calculate the sample mean in each case and show that as n increases the sample mean approaches the true population mean. Reminder: The "RNORMAL" function in R: RNORMAL (# sample size, mean = # population mean: sd = # population standard deviation)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
Please solve the question with R studio or show calculation steps, thank you. Do not randomly write wrong answers if don't know how to solve.
![**Q2) Example with a Normal Random Variable: Turn in the Printout**
Suppose the random variable "height" has a normal distribution with mean 67 and variance of 14. Use the `rnorm()` function to draw three random samples from this population with the sizes 10, 1000, and 1,000,000 respectively. Calculate the sample mean in each case and show that as n increases, the sample mean approaches the true population mean.
**Reminder:** The `RNORMAL` function in R:
```
RNORMAL(# sample size, mean = # population mean, sd = # population standard deviation)
```
**Use R to Illustrate the Central Limit Theorem**
The "central limit theorem" states that as n increases,
\[
\frac{\bar{X} - E(X)}{\sqrt{\frac{V(X)}{n}}}
\]
approaches standard normal.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc1e78592-0bf4-4b47-9b18-d7a6fa476d06%2F500b6bc3-c40e-46b5-99d4-5ece08dde2bc%2F0o3s3gj_processed.png&w=3840&q=75)
Transcribed Image Text:**Q2) Example with a Normal Random Variable: Turn in the Printout**
Suppose the random variable "height" has a normal distribution with mean 67 and variance of 14. Use the `rnorm()` function to draw three random samples from this population with the sizes 10, 1000, and 1,000,000 respectively. Calculate the sample mean in each case and show that as n increases, the sample mean approaches the true population mean.
**Reminder:** The `RNORMAL` function in R:
```
RNORMAL(# sample size, mean = # population mean, sd = # population standard deviation)
```
**Use R to Illustrate the Central Limit Theorem**
The "central limit theorem" states that as n increases,
\[
\frac{\bar{X} - E(X)}{\sqrt{\frac{V(X)}{n}}}
\]
approaches standard normal.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 7 images
Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman